Jet lag, medical imaging, brain disorder treatment could see benefits
An engineer at Washington University in St. Louis plans to develop principles that could be used to control the collective behavior of individuals in a group that could ultimately be applied to yield high-resolution medical images, reduce jet lag, stabilize power systems and shed light on advancing brain-stimulation technology.
Pattern Formation for a Population System: The design of a global input that transforms the dynamic pattern in an ensemble of harmonic oscillators - from a star to a maple leaf.
Jr-Shin Li, Professor in the School of Engineering & Applied Science, will develop these principles with a three-year, $589,486 grant from the Air Force Office of Scientific Research. While the work is theoretical and computational, Li says the goal is to understand the fundamental limits on the ability to control the dynamics of a group or a population system. Li's group has extensive and close collaboration with biologists, chemists and applied physicists. The methods they develop will be tested and validated experimentally on cellular networks, chemical networks, mice and bees.
"The common thread is that we're trying to manipulate dynamic patterns or structures, such as synchrony," says Li, a faculty member in the Preston M. Green Department of Electrical & Systems Engineering. "A typical goal is to design one global or a few sparsely distributed inputs to change the dynamics and encode spatiotemporal information of a complex system constituted by an ensemble of dynamical units as desired."
For example, using light may help reset the circadian rhythm to reduce jet lag, using brain stimulation may help reset the neuronal system behind Parkinson's disease, and using electromagnetic pulses may help enhance sensitivity in high resolution nuclear magnetic resonance spectroscopy and imaging.
The major challenge in the control of ensemble or population systems is that one cannot send control signals to each individual system in the ensemble, but only to the ensemble as a whole, Li said.
"In the brain, there are billions of neurons, and in magnetic resonance applications, there are 10 to the 23rd power," he says. "It is hard to imagine how to manipulate such a huge number of systems simultaneously, for example, for pattern formation and for inducing synchronization or stability."
Li has already done some early work in this area. In his lab, he designed an input that changed the pattern of a group of harmonic oscillators from a star to a maple leaf. While it might sound simple, Li asserts that it is a very challenging problem to solve and an algorithm to design to compute the optimal input.
Li's research focuses on dynamics and control, optimization and computational mathematics, and machine and dynamic learning. In particular, he is interested in studying complex systems arising from emerging physical, biological and medical applications. In 2010, Li received a Young Investigator Award from the AFOSR, and in 2008 received a National Science Foundation Career Award.
The School of Engineering & Applied Science at Washington University in St. Louis focuses intellectual efforts through a new convergence paradigm and builds on strengths, particularly as applied to medicine and health, energy and environment, entrepreneurship and security. With 96.5 tenured/tenure-track and 28 additional full-time faculty, 1,200 undergraduate students, 1,200 graduate students and 20,000 alumni, we are working to leverage our partnerships with academic and industry partners — across disciplines and across the world — to contribute to solving the greatest global challenges of the 21st century.